UV map slightly distorted for some reason
About your distorted UV map:

it comes from the fact that your beam is actually enlarging on its top, so the faces are not perpendicular. The consequence is that it will stretch the UV map in the UV Editor: Blender just tries to find an average arrangement between faces, it doesn't know that it needs to give priority to perpendicular angles. I've made a second test with perpendicular faces and as you see it works fine.

What you could do though is making the UV map orthogonal with some addons, or: first unwrap the top part, then the bottom, then in the UV Editor, make the bottom faces stick to the top faces with the help of the snap.



About your Bake problem:

There might be several reasons, it really depends on your problem. I guess one of your problems is that your object is made of 90° perpendicular angles. In that case you need to know that, as the ray of the baking follows a direction that is perpendicular to the face normal, it won't be able to record any of the faces that are completely parallel or perpendicular... the baking will be completely "blank". Whereas if you slightly tilt those parallel faces the ray will hurt them and therefore they will be seen (the perpendicular face won't be seen but it doesn't matter, the parallel faces will give the illusion of deepness).